Is it possible to add modifiers dynamically with animation nodes?
The only way to do this is by using scripting, there are three important points to take into consideration when making this:


Make sure not to add the modifier if it was already added in a previous execution.
Output the input object and plug it into the attribute output node, making sure you are not editing a modifier before it gets added.
The modifier name should never be an empty text because then blender will automatically add a name and our first test will fail, so we should set a fallback value.


Making sure we got those three points right, we can write a code like this:

modifierName = modifierName if modifierName != "" else "Fallback"
if not modifierName in object.modifiers:
    object.modifiers.new(modifierName, 'ARRAY')
outObject = object